grazing incidence x-ray scattering and diffraction synew/portale.pdf · grazing incident small...
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Giuseppe PortaleNWO, DUBBLE@ESRF
European Synchrotron Radiation FacilityGrenoble (France)
Grazing Incidence X-ray Scattering and DiffractionTheory and applications
Mini-school, Uthecht June 2, 2015
Outline
• Experimental considerations
• Brief introduction to the Distorted Wave Born Approximation
• Example GISAXS
• GIWAXS + example
Transmission vs Gracing incidence geometry
Sample
X-rays
1
10
100
1000
104
105
106
107
0.2 0.4 0.6 0.8 1 1.2 1.4
SiO2 R=25nm
monodisperse
polydisperse
Inte
nsity (
a.u
.)
q (nm-1
)
Transmission:
Gracing incidence:
Experimental setup & conventions
It
Io
ai
f
Bent mirrorS3
S2
S1
Mono
Ideally, beam as small as possible vertically and parallel
Grazing Incident Small Angle X-ray Scattering
Characterization of nanoscale density correlations and/or the shape of nanoscopic objects at surfaces, at buried interfaces, or in thin films
• Surface sensitive (minimum penetration depth 10 nm)
• 2D-GISAXS: lateral and normal ordering probed at the same time
• Complex data analysis𝑞𝑥,𝑦,𝑧 =
2𝜋
𝜆
cos 𝛼𝑓 cos 2𝜃𝑓 − cos(𝛼𝑖)
cos 𝛼𝑓 sin 2𝜃𝑓
sin 𝛼𝑓 +sin 𝛼𝑖
• Surface sensitive – possibility to study structures at the interfaces
• High scattering intensity ideal to perform in-situ and time-resolved study
Image: Prof. Andreas Meyer, Uni Hambourg
X-ray reflectivity (XRR)
• Measure strictly only along 𝑞𝑧 =4𝜋
𝜆sin 𝛼
• Point detector with collimator
• Information about re(z), roughness, thickness
10-5
0.0001
0.001
0.01
0.1
1
0 0.5 1 1.5 2
Re
flectivity
qz (nm
-1)
0.001
0.01
0.1
1
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0.1 0.15 0.2 0.25 0.3 0.35
Refle
ctivity
qz (nm
-1)
Angle (o)
ac SiO2
ac PS
Usually in GIXS ac (polym) < ai < ac (sub)
Regimes for GISAXS analysis
ai < ac (polymer) : evanescent regime
ac (polymer) < ai < ac (substrate) : dynamic regime
ai > ac (substrate) : kinematic regime
In the kinematic regime:𝑑𝜎
𝑑Ω(𝒒) =
1
𝑁
𝑖
𝑗
𝐹𝑖 𝒒 𝐹𝑗,∗ 𝒒 𝑒𝑥𝑝 𝑖𝒒(𝑹∥𝑖 − 𝑹∥
𝑗)
In the simple Born Approximation (BA): 𝐹𝑖 = 𝑉
ρ(𝐫)exp 𝑖𝒒 ∙ 𝒓 𝑑𝒓
Horizon line
Experimental considerations
Footprint of the beam:
Beam 300 mm:ai = 0.1° 17 cmai = 0.5° 3.4 cm
ai
Surface scattering – reflection and refraction
Light
Index of refraction: n ≥ 1
a
a’
X-ray
Index of refraction: n = 1 – d + ib
ai > ac
a
ai < ac af = ai
Total reflection
Snell’s law: n1sin a = n2 sin a ’
Snell’s law: n1cos a = n2 cos a ’
n1
n2
Surface sensitivity (penetration depth)
Limited penetration into the sample enhanced surface sensitivity
10
100
1000
104
105
106
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Penetration depth - (Å)
Si
Au
PP
(
Å)
ai / a
c
Snell’s law: cos a = n cos a ’
Critical angle: 2 /c era d r
12 keV ( = 1.033 Å)
For ai ≤ ac
Evanescent regime
Reflection and Transmission coefficients
For the bare substrate: E r, k = 𝐸0𝑒−𝑖𝑘∥𝑟∥
𝑒−𝑖𝑘𝑖,𝑧𝑧 + 𝑟𝑒𝑖𝑘𝑖,𝑧𝑧 𝑓𝑜𝑟 𝑧 > 0
𝑡𝑒−𝑖𝑘t,𝑧𝑧 𝑓𝑜𝑟 𝑧 < 0
𝑟 =𝑘𝑖,𝑧 − 𝑘𝑡,𝑧𝑘𝑖,𝑧 + 𝑘𝑡,𝑧
𝑡 =2𝑘𝑡,𝑧𝑘𝑖,𝑧 + 𝑘𝑡,𝑧
Fresnel reflectivity: 𝑅𝐹 = 𝑟2
Fresnel transmission: 𝑇𝐹 = 𝑡2
Yoneda peak
𝑛 = 1 − 𝛿 + 𝑖𝛽
Nano-objects supported on a substrate
𝑑𝜎
𝑑Ω= 𝑟𝑒2 Δ𝜌 2 ℱ(𝒒∥, 𝑘𝑧
𝑖 , 𝑘𝑧𝑓)2
𝒒 = 𝒌𝑓 − 𝒌𝑖
𝑞𝑧1 = 𝑘𝑧
𝑓− 𝑘𝑧𝑖
1
𝑞𝑧2 = 𝑘𝑧
𝑓+ 𝑘𝑧𝑖
2
ai
𝑞𝑧3 = −𝑘𝑧
𝑓− 𝑘𝑧𝑖
3
af
𝑞𝑧4 = −𝑘𝑧
𝑓+ 𝑘𝑧𝑖
4
ℱ 𝒒∥, 𝑘𝑧𝑖 , 𝑘𝑧𝑓= 𝐹(𝒒∥, 𝑞𝑧
1) +𝑟(𝛼𝑖)𝐹(𝒒∥, 𝑞𝑧2) +𝑟(𝛼𝑓)𝐹(𝒒∥, 𝑞𝑧
3) +𝑟(𝛼𝑖)𝑟(𝛼𝑓)𝐹(𝒒∥, 𝑞𝑧2)
Classican Born Approx. (SAXS)
Distorted Wave Born Approximation - DWBA
For a simple sphere:
𝐹𝑠𝑝ℎ𝑒𝑟𝑒 𝑞, 𝑅 = 4𝜋𝑅3sin 𝑞𝑅 − 𝑞𝑅𝑐𝑜𝑠(𝑞𝑅)
(𝑞𝑅)3𝑒𝑖𝑞𝑧𝑟
Classical SAXS
Nano-objects supported on a substrate
1
2
3
4
Si substrate
PS bead R = 5nm
Yoneda peak for Si substrate: af = ac
Nano-objects supported on a substrate: effect of increasing ai
0.1° 0.2° 0.3° 0.4°0.15°
Au nanoparticles R = 25nm on glass substrate
For supported nano-object the maximum scattered intensity is at the critical angle of the substrate
Particle shape sensitivity
Calculations performed using the IsGISAXS software (R. Lazzari)
𝑞𝑥,𝑦,𝑧 =2𝜋
𝜆
cos 𝛼𝑓 cos 2𝜃𝑓 − cos(𝛼𝑖)
cos 𝛼𝑓 sin 2𝜃𝑓
sin 𝛼𝑓 +sin 𝛼𝑖
Calculated form factors under the DWBA
Renaud G., Lazzari R., Leroy F., Surf. Sci Rep. 64 (2009), 255-380
Now with spatial correlation between nano-objects
If spatial correlation exists between objects, an interference function has to be considered:
Decoupling approximation (DA):
Local monodisperse approximation (LMA):
𝐼 𝑞 ∝ 𝐼𝑑 𝑞 + 𝐹 𝑞2𝑆(𝑞)
𝐼 𝑞 ∝ 𝐹 𝑞 2 𝑆(𝑞)
PS cylinders with 2D hexagonal latticePS spheres with 2D hexagonal lattice
q* 3q* 4q*
Supported nanoparticles: Pt deposit on MgO (001)
J. Olander et al. Phys. Rev. B 76 (2007) 075409.
TEM
Disks with 1D paracrystalline lattice
Au clusters on a substrate@BM26B
Au clusters with R = 3nm and H/R = 1.6
H
2R
10
100
0 1 2 3 4 5
Au:Ag 20:80
ai = 0.13
o
Fit
Inte
nsity (
a.u
.)
qy (nm
-1)
10
100
0 1 2 3 4 5 6
Au:Ag 20:80
ai = 0.13
o
Fit
Inte
nsity (
a.u
.)
qz (nm
-1)
GISAXS from a monolayer of core-shell gold-PNIPAM nanoparticles
10
100
1000
104
105
106
107
108
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
0.1o
Sim. IsGISAXS
Inte
nsity
qy (nm
-1)
Spheroidal Gold coresR = 25nm
2D Hex witha = 230 nm
a
High resolution GISAXS (GIUSAXS)
-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
Standard GISAXS
High resolutionGIUSAXS
Inte
nsity (
a.u
.)
qy (nm
-1)
0th order
1st order
7th
order
q* = 0.0048 nm-1 d = 1.3 mm
AFM GIUSAXS
Au linear assembly
Buried interfaces: Pb clusters implanted in Si substrate
0
5
10
15
20
25
-1,5 -1 -0,5 0 0,5 1 1,5
sample 2
Inte
nsity (
a.u
.)
qy (nm
-1)
ai ~ ac (substrate) ai >> ac (substrate)
Dintercluster = 9nm
x x
Scattering from facets: Ge/Si(001) quantum dots
A.V. Zozulya, et al. Phys. Rev. B 78 (2008) 121304
Bragg rod is proportional to the facet area
Laser Induced Periodic Surface Structures (LIPSS)
Film surface
so : Molecular Roughnessll : longest wavelengthls : shortest wavelength
• Roughness :
C. Bollinne, S. Cuenot, B. Nysten, and A.M. Jonas. Eur. Phys. J. E 12, 389–396 (2003).Z. Guosheng, P.M. Fauchet, A.E. Siegman. Phys. Rev. B, 5366 (1982)
Laser beam • Interference of the incident and reflected light at
the interface produces Ripples with a period L :
isin
n
l: light wavelength: angle of incidence n : refraction index
In-situ GISAXS: study of LIPSS formation
ai
af
w
ai
LIPSS Film
Film LIPPS
H
2R2W
=
AFM
T. Etzquerra (CSIC Madrid)
(a) (b)(a) (b)
Poly(tri methylene terephthalate)(PTT)
•
Mirrors
Sample
I
A
I: IrisA: Attenuator
Laser
00306090120210310
F=7 mJ/cm2 @ N pulses (8ns)
N pulses (8ns)
Set-up @ BM26, ESRF
Final height about 50nm, periodicity about 200 nm
-90 nm
-50 nm
50 nm
-50 nm
60 nm
80 nm
-80 nm
80 nm
10 nm
0 nm
5 nm
0 nm
2 nm
0 nm
5 nm
0 nm
5 nm
-70 nm
0 nm
2 nm
-2 nm
40 nm
0 nm
40 nm
-20 nm
20 nm
0 nm
50 nm
(a) Non-irrad.
(b) 4 mJ/cm2
(c) 5 mJ/cm2
(d) 6 mJ/cm2
(e) 8 mJ/cm2
(f) 10 mJ/cm2
(g) 14 mJ/cm2
(b) 100 (c) 300
PTT_sc_3_9
100 vs nanometros_PTT_sc_3_9
0 (mm) 2
160
0nm
PTT_sc_3_2
X Data
h(nm)
300 vs nanometros_PTT_sc_3_2
0 (mm) 2
160
0nm
(d) 600 (e) 1200 (f) 6000
PTT_sc_3_1
X Data
h(nm)
600 vs nm_PTT_sc_3_1
0 (mm) 2
160
0nm
2D Graph 5
X Data
h(nm)
1200 vs nm_PTT_sc_2_3
0 (mm) 2
160
0nm
2D Graph 6
X Data
h(nm)
6000_ripples vs PTT_sc_1_8
0 (mm) 2
160
0nm
PTT_sc_2
X Data
Y Data
0 vs PTT_sc_2 0 (mm) 2
160
0nm
AFM F=7 mJ/cm2 @ N pulses (8ns)5x5 mm2
GISAXS at the liquid-air interface
Colloidal CdSe/CdS nanorods
F. Pietra et al. Nano Letters 12 (2012) 5515-5523
Deflecting crystal
Adjustable z-table
GIWAXS – crystallinity and orientation
Isotropic:
Textured – slightly oriented:
Highly oriented:
Detector
Rings
Arcs
Spots
GIWAXS (1) - Block-copolymer additives in OPVs
Why P3HT- b -P4VP:non-covalent supramolecular interactions between P4VP and PCBM
P3HT- b -P4VP is blended with P3HT:PCBM
Inverted OPV devices◉ Glass/ITO/TiOx/active layer/MoO3/Ag
Goal:◉ Exploit the PCBM - P4VP interactions to trigger the morphology and
improve the power conversion efficiency (PCE)
P3HT:PCBM:P3HT-b-P4VP blends
as cast devices annealed
Prof. G. Hadziioannou (Uni Bordeaux)
* Adv. Mat. 2012, 24, 2196-2201
P3HT- b -P4VP as nanostructuring agent in the P3HT:PCBM blend*
0.5 1.0 1.5 2.0
q [Å-1]
P3HT:PCBM
+4% P3HT-b-P4VP
P3H
T (
10
0)
PC
BM
P3H
T (
01
0)
PC
BM
P3H
T (
10
0)
Inte
nsity (
a.u
.)
qxy
[Å-1]
P3H
T (
20
0)
P3H
T (
10
0)
qz [Å
-1]
Upon P3HT- b -P4VP incorporation:
• PCBM is less aggregated → more interfaces for exciton
dissociation
• Minor decrease in the crystallinity of P3HT
• Increase in the population of the face-on oriented P3HT
crystallites
GIWAXS (1) - Block-copolymer additives in OPVs
GIWAXS (2) – Ordering in organic thin film transistors
Yoneda peak
(001) peak
(002) peak
Low angle diffuse scattering
qy (nm-1)
qz
(nm
-1)
GIWAXS
001002
010
GISAXS
MM1320 (5 nm)MM1325 (50 nm)
GIWAXS (2) – Ordering in organic thin film transistors
qy (nm-1)
qz
(nm
-1)
qy (nm-1)
qz
(nm
-1)
qy (nm-
1)q
z(n
m-1
)
001
0020
10
MM1322 (15 nm)
<001>
Software for DWBA
• IsGISAXS from R. Lazzary (Windows)R. Lazzari, (U. Curie, Paris) J. Appl. Cryst. 35:406-21 (2002)
• FitGISAXS from D. Babboneau (Igor Pro)D. Babboneau (U. Poitiers) J. Appl. Cryst. 43 929-936 (2010)
• BornAgain (Python)C. Durniak et al, (Juelich)
1. Als-Nielsen, Jens, and Des McMorrow. Elements of modern X-ray physics. John Wiley & Sons, (2011).
2. Daillant, J., and A. Gibaud. "X-ray and Neutron Reflectivity and Scattering." (1999).
3. Müller-Buschbaum, P. "Grazing incidence small-angle X-ray scattering: an advanced scattering technique for the investigation of nanostructured polymer films." Analytical and bioanalytical chemistry 376.1 (2003): 3-10.
4. Renaud, Gilles, Rémi Lazzari, and Frédéric Leroy. "Probing surface and interface morphology with grazing incidence small angle X-ray scattering." Surface Science Reports 64.8 (2009): 255-380.
Books and references
Conclusions
• GISAXS and GIWAXS are powerful tools to obtain statistical structural information on sub-monolayers, monolayers and multilayers of soft and hard condensed matter
• GISAXS 1-100 (1000) nm
• GIWAXS down to 0.1 nm
• Surface sensitivity
• High intensity allows for in-situ study
Thank you for your attention!
Questions?